Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

The Two Cultures of Mathematics (2000) [pdf]

dpmms.cam.ac.uk

Post reply on HN
Print view View original

31–40 of 72 posts

Re: The Two Cultures of Mathematics (2000) [pdf]

#31

Post by eru »

6gvONxR4sf7o wrote: post #17
josephg wrote: post #16

Earlier quoted context omitted.

I'd love to see actual numbers on this. Its not 95% - but all of our intuitions will be a bit wrong because people cluster in workplaces based on personal values. So no matter what you're like, you'll end up working with people similar to yourself. I wouldn't be surprised if people who just program for a paycheck are the majority of employees in many offices. I know they're a tiny minority in a lot of the places I've…

> I'm not sure it makes sense to describe people who love programming and people who just do it for a paycheck as truly being in the same field. This is why I keep my mouth shut IRL about just wanting the paycheck. I'd imagine a lot more than a tiny minority of people are just there for the job where you've worked. We just keep our mouths shut because the passionate folks judge us paycheckers.

It's fine to optimize for the paycheck first and foremost.

But while you are at your job anyway, might as well make it slightly less of a drudgery while you are at it.

(Eg I quite like functional programming. Both because I like the style of thinking, but also because I don't trust myself nor anyone else with code; and eg a heavy emphasis on immutability means that I'm less likely to get woken up in the middle of the night with some production problem.)

Re: The Two Cultures of Mathematics (2000) [pdf]

#32

Post by globular-toast »

josephg wrote: post #11

I wrote a blog post a few years ago[1] making a similar claim about computer science. I said there’s 3 main camps of programmers: - People who enjoy programming because it’s mathematically beautiful (eg Haskell programmers) - People who enjoy programming because they like reasoning about machines, and like mechanical sympathy (eg C programmers) - And people who like programming because it can solve real problems for…

For me, these are three different hats that I keep on my hatstand. I like them all. The dream is to wear all three at once and get paid for it. But, in practice, I'm always wearing hat 3 when I'm getting paid and, if I'm lucky, I can put on one of the other two for a while too. However, I have worked with many people who appear to never switch hats.

Re: The Two Cultures of Mathematics (2000) [pdf]

#33

Post by alberto_ol »

dang wrote: post #15

Some past threads: The two cultures of mathematics and biology - https://news.ycombinator.com/item?id=8819811 - Dec 2014 (69 comments) The Two Cultures of Mathematics (2000) [pdf] - https://news.ycombinator.com/item?id=7970284 - July 2014 (28 comments) "Problem Solvers" vs "Theory Developers": The Two Cultures of Mathematics. [pdf] - https://news.ycombinator.com/item?id=682913 - July 2009 (5 comments)

the first thred "The two cultures of mathematics and biology" is not the same essay

Re: The Two Cultures of Mathematics (2000) [pdf]

#34

Post by isolli »

Only tangentially related, but a friend of mine had to interrupt his doctoral thesis in mathematics because the set he was studying turned out to be empty. This gave a lot of ammunition to our Russian colleagues, who routinely make fun of French mathematicians for being far too ensconced in theory.

Re: The Two Cultures of Mathematics (2000) [pdf]

#35

Post by Karrot_Kream »

josephg wrote: post #11

I wrote a blog post a few years ago[1] making a similar claim about computer science. I said there’s 3 main camps of programmers: - People who enjoy programming because it’s mathematically beautiful (eg Haskell programmers) - People who enjoy programming because they like reasoning about machines, and like mechanical sympathy (eg C programmers) - And people who like programming because it can solve real problems for…

Fantastic! Thanks for this. The FP vs non-FP split has always just felt like a less rigorous version of the "analysis vs algebra" or "problem-solving vs theoretical" discussion and I'm glad I'm not alone in thinking this.

This is also what rubs me the wrong way about the simplistic level with which FP languages (like Haskell or Scala+monads) are either cargo culted or hated. The truth is, the two perspectives really go hand-in-hand, and we're all the worse for not realizing this.

Re: The Two Cultures of Mathematics (2000) [pdf]

#36

Post by rocqua »

graycat wrote: post #4
throwaway17_17 wrote: post #2

I feel like I could sit down and rewrite this, in a couple of hours, to be about Computer Science, but the practical field and the educational as well. I mean, I could feasibly include this sentence as a quote, depending on which aspect of CS I was talking about (academic CS and language design in particular): ‘It is that the subjects that appeal to theory-builders are, at the moment, much more fashionable than the o…

From my experience, among academic computer science professors, the attitude is that computer science is about the "fundamentals" of computing. E.g., once I was talking with such a computer science professor and listing features I wanted in a better programming language, and immediately his reaction was that for a professor developing such a language would be "academic suicide".

My university had an amazing C++ programming course. Essentially all STEM majors could take credits from the course. CS did not allow credits from this course because "It is just programming" it teaches nothing fundamental.

Meanwhile, this course was more difficult that most other courses, taught me to code much better, which helped most other courses, and taught me basic principles that I easily generalized and re-applied in other CS courses. I think that a lot of people going to do Academic work would have been better of for having taken this course. Even if they never were to touch a C++ like language again.

The fact that, when talking about inheritance and sub-typing in C++, the terms "variance" or "co-variance" never came up, does not mean that this course taught me little on type-theory.

Re: The Two Cultures of Mathematics (2000) [pdf]

#37

Post by stared »

josephg wrote: post #11

I wrote a blog post a few years ago[1] making a similar claim about computer science. I said there’s 3 main camps of programmers: - People who enjoy programming because it’s mathematically beautiful (eg Haskell programmers) - People who enjoy programming because they like reasoning about machines, and like mechanical sympathy (eg C programmers) - And people who like programming because it can solve real problems for…

The camp 3 is called "professional programmers". I mean:

- sometimes a practical problem benefits greatly from a well-designed high-level abstraction,

- sometimes a practical problem strictly requires low-level optimization.

And yes, it is totally fine to have one's inclination in general, pursue them to any level in their free time, or in some (but not all) academic research. Yet, if a professional software engineer consistently favours one of these motivations over adding value to the product, usually there are frictions in the workplace.

I guess you all know "let's rewrite it to Haskell" people, or ones using their favourite paradigm for everything, and against everyone. Or ones that squeeze 20% performance in a place of code that does not matter at all for the end user experience.

Re: The Two Cultures of Mathematics (2000) [pdf]

#38

Post by piadista »

Actually the late Prof Leo Breiman expanded this metaphor into the statistical modelling world. The two cultures being the explanatory and predictive modelling folk.

The explanatory modelling culture (that he calls the data modelling culture) being those that first come up with a guess of how the data is generated and then try to test that hypothesis using goodness of fit measures, and the predictive modelling culture (he calls algorithmic modelling culture) being the modern machine learning researchers that are purely interested in predictive power.

The full essay is here: https://projecteuclid.org/journals/statistical-science/volum...

Re: The Two Cultures of Mathematics (2000) [pdf]

#39

Post by ukj »

This paper makes a ton of brilliant points all of which strongly resonate with me:

* The results that will last are the ones that can be organized coherently and explained economically to future generations (yes! effective compression!)

* How effectively a result can be communicated to another mathematician (and perhaps even s/mathematician/person/)

90% of my time spend 'studying mathematics' is spent lexing the notation. What do those symbols even mean? I can't even copy-paste this into Google to get any meaningful results!!!!!!!!!!!!@#!$@#$@#$@#$#@!$@#$

Have you noticed how we don't have this problem in Computer Science? Because the source code gives you the context in which to interpret the meaning of the grammar!

Homoiconicity is the panacea of formal languages.

Re: The Two Cultures of Mathematics (2000) [pdf]

#40

Post by GoblinSlayer »

brokenkebab wrote: post #22
29athrowaway wrote: post #13

Earlier quoted context omitted.

And people that do not care about any of those things and just want a paycheck, or to be promoted so that they do not have to code anymore (95% of developers worldwide). Unfortunately the people that get excited building things is outnumbered by the people that is just in this for the money.

>Unfortunately the people that get excited building things is outnumbered by the people that is just in this for the money. I don't think there's a reason to be sad about it. There are plenty of e.g. maintenance jobs in the industry, and people who are passionate about programming may not be the best fit for this niche - it's boring, and sometimes you feel the urge to re-invent a few wheels even in detriment to actua…

There's no real difference, if your sole interest is a paycheck, any programming is boring.
Post reply on HN